Hi DaLeKo,
Your translation has the word "divorce" in verse 3, but the word in the Greek text, according to Strong's, is
apoluō and is translated "
put way" in the KJV and a few other translations.
Remember that the Pharisees were trying to "tempt" Jesus with their question. They were not asking Jesus about divorce, but about men
putting away their wives
for any reason and that is what He responded to.
THEN, the Pharisees asked: "
Why did Moses then command to give a writing of divorcement, and to put her away?"
.... but the question was still about men
putting away their wives and that is what Jesus responded to:
Moses suffered the men to put away their wives for any reason even before he commanded them to begin giving them a bill of divorcement so that they were free to remarry without committing adultery (the penalty for which was death).
Jesus did not reverse this, or say that Moses did anything wrong in commanding the men to divorce their wives if they were going to put them away for reasons other than fornication. He simply addressed the question that the Pharisees asked and that was about men "putting away" their wives for any reason.
If they were one and the same things (ie putting away = divorce) then what need would their have been to differentiate between who did or did not have "a writing (or bill) of divorcement"?